surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...

, free stationing (also known as resection) is a method of determining a location of one unknown point in relation to known points. There is a zero point of reference called a

total station A total station (TS) or total station theodolite (TST) is an electronic/optical instrument used for surveying and building construction. It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure b ...

. The instrument can be freely positioned so that all survey points are at a suitable sight from the instrument. Setting up the total station on a known point, often it is not possible to see all survey points. With the total station, bearings and distances are measured to at least two known points of a

control network A geodetic control network (also geodetic network, reference network, control point network, or control network) is a network, often of triangles, which are measured precisely by techniques of terrestrial surveying or by satellite geodesy. ...

. This with a

handheld computer A mobile device (or handheld computer) is a computer small enough to hold and operate in the hand. Mobile devices typically have a flat LCD or OLED screen, a touchscreen interface, and digital or physical buttons. They may also have a physical k ...

recorded data is related to local

polar coordinates In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to th ...

, defined by the horizontal circle of the total station. By a

geometric transformation In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often b ...

, these polar coordinates are transformed to the coordinate system of the control network. Errors are distributed by

least squares adjustment Least-squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals. It is used extensively in the disciplines of surveying, geodesy, and photogrammetry—th ...

. The position and orientation of the total station in relation to where the

is established.

Comparison of methods

* Angular resection and

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...

: only bearings are measured to the known points. *

Trilateration Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth ( geopositioning). When more than three distances are involved, it may be called multilateration, for ...

: only distances are measured to the known points. * Free stationing and triangulateration: both bearings and distances are measured to the known points.

Naming

Because bearings and distances in a resection (free stationing) are measured, the result may have a different mathematical solution. This method of a "total station set up" has different names in other languages, e.g. German: :de:Freie Standpunktwahl (free stationing). Naming is also regulated by the

German Institute for Standardization German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law ** ...

DIN 18 709.

Different mathematical solution

By measuring bearings and distances, local

are recorded. The orientation of this local polar coordinate system is defined by the 0° horizontal circle of the total station (polar axis L). The pole of this local polar coordinate system is the

vertical axis A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...

(pole O) of the total stations. The polar coordinates (r,f) with the pole are transformed with a surveying software in a data collector to the

Cartesian coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured i ...

(x,y) of the known points and the coordinates for the position of the total station are calculated. In a resection (triangulation) measuring bearings only, there can be a problem with an infinite number of solutions called: " danger circle" or " inscribed angle theorem".

Back-sight points

The back-sight points of the control network should cover and surround the stationing site. The position of the total station is not part of the area. This is the area where you want to measure with this station setup. Topographic points or stakeout points should not be measured outside this area. If measured outside this area, the errors in orientation will be extrapolated instead of being interpolated. While it is possible to use only two known control points in a resection (free stationing), it is recommended to use three control points. There is no redundancy for orientation, using two points only. Using five or more points of the control network, there is only a slight improvement in the accuracy.

Advantages

* Choose the station point free for best visibility to all survey points * Where there is no obstruction * Where there is no traffic * Where there is the highest safety for the observer and the instrument Because of the range and accuracy of total stations, the method of a resection (free stationing) permits a great freedom of positioning the total station. For this reason, this method is one of the most used station set ups.

Application

With the calculated coordinates and orientation of the total station, it can be used to set out points in

construction surveying Construction surveying or building surveying (otherwise known as "staking", "stake-out", "lay-out", "setting-out" or "BS") is to stake out reference points and markers that will guide the construction of new structures such as roads or buildings. T ...

, machine guidance,

site plan A site plan or a plot plan is a type of drawing used by architects, landscape architects, urban planners, and engineers which shows existing and proposed conditions for a given area, typically a parcel of land which is to be modified. Sites pl ...

or other types of surveys.

References

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External links

Topcon Magnet Field 1.0 Help

Leica SmartWorx Viva Field Software Datasheet

CarlsonSurvCE Reference Manual

12d Field – Helmert Resection

Trimble: Advantages and Disadvantages of the Stationing Programs

Trimble: Neighborhood Adjustment
Surveying Surveying instruments Geodesy Civil engineering